Local-in-time adjoint-based topology optimization of unsteady fluid flows using the lattice Boltzmann method

This paper presents a local-in-time (LT) discrete adjoint-based topology optimization method for unsteady incompressible viscous flows incorporating the lattice Boltzmann method (LBM). For the optimization of unsteady flows, straightforward global implementations of the time-dependent optimization are usually adopted. However, such global implementations require that the entire flow solution history be available to calculate the solution of the adjoint equation reversed in time. For 3-D design optimization problems, the storage requirements can become prohibitively large. In this paper, the LT discrete adjoint-based method is applied to a LBM-based topology optimization to reduce the storage requirement. The basic idea of the LT method is to divide the entire time interval into several subintervals and to approximate the global sensitivity derivative as a combination of local sensitivity derivatives computed for each time subinterval. In this approach, flow solutions for only a single subinterval need to be stored. Since each time subinterval includes only a few (possibly one) time steps, the data storage requirements can be tremendously reduced. This method is applied in a pressure drop minimization problem considering unsteady viscous fluid. Two- and three-dimensional numerical examples are provided to confirm the validity and utility of the presented method